When was the catalytic converter last changed?  Old cars are often
have this problem because rhe new owner doesn't know how old the cat
is.

Your symptoms are consistent with a degraded cat that has loose broken
piece(s) of catalyst which block the exhuast path when enough exhaust
flow is created (full throttle), the back pressure which results will
stall the engine.  It's like "a banana in the tailpipe".

Michael

Sounds like a fuel quantity/mixture problem.  I'd consider checking
the fuel rail and fuel pressure regulator to see enough fuel is
getting through.  It's also possible you have a vacuum leak that opens
under acceleration, leaning out the mixture.  The big rubber intake
boot between the manifold and the FI unit would be a suspect here -
not an uncommon failure of an easily-replaced $30 part.

If you don't have a good manual, you need one.  Don't know if Bentley
does an E30 manual.  For this problem, though, you could check the
Bentley 5 Series manual for the E28 because it's the same engine as in
the 528e.
--
C.R. Krieger
(Been there; done that)